Dasani has been sharing one room with her parents and seven brothers and sisters. One brother is legally blind and two of her sisters are asthmatic. Her parents use methadone to stay off heroin, which can leave them in a stupor.

The family's single room is overrun with mice. Nothing stops them, not even traps or hanging food from the ceiling in plastic bags. The shelter is no place for children. In addition to the mice, there is exposed asbestos and lead paint. The smoke detectors and alarms are broken.

The family stands in line in the cafeteria for packaged meals then stands in another line to use one of two microwaves. When Dasani's mother smuggled an old microwave she had found into their room, the shelter staff confiscated it.

There are more than 50,000 people in the New York City shelter system, the most since the Great Depression. We don't know how many more people are sleeping on a relative's couch or floor. You can't even get into the shelters if a family member or friend will take you in.

At least one person is working in 28 percent of shelter families. Among single individuals, 16 percent are working. But they still can't make enough to get out of the shelters.

Even if both of Dasani's parents were working minimum-wage jobs, they would only make $2,300 a month. That would just cover the rent on a one-room apartment for 10 people.

New York's last mayor, billionaire Michael Bloomberg, made things much worse for homeless people. He told The New York Times that shelters offered homeless families "a much more pleasurable experience than they ever had before." In an interview about the Times series with the Politicker website, Bloomberg said that Dasani "was dealt a bad hand. I don't know quite why. That's just the way God works. Sometimes, some of us are lucky, and some of us are not."

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WE'LL HAVE to see what Bloomberg's successor, liberal Democrat Bill de Blasio, will do for homeless and low-income New Yorkers.

Homeless people need many things, including jobs, income and social services. But without affordable housing, they'll still be stuck in the shelters. De Blasio has promised to get homeless people out of the shelters and create or preserve affordable housing for low- and moderate-income families.

If de Blasio gives homeless people the first priority in public housing, some people could leave the shelters almost immediately. Unfortunately, this will only help a relative few. The New York City Housing Authority is so drastically underfunded that it has hundreds of apartments vacant because they need repairs or rehabilitation.

De Blasio proposes to create new affordable housing--some of which might even help people get out of the shelters--through what is known as mandatory inclusionary zoning, and investing $1 billion from city workers' pension funds in building affordable housing.

Mandatory inclusionary zoning means that when developers need city permission to build new housing, they'll have to include some apartments that low- and moderate-income people can afford. To get private developers to build affordable apartments, the city will have to bribe them with permission to build many more market-rate units--in reality, luxury apartments that very few working New Yorkers can afford.

Under de Blasio's plan, which was created by the Association for Housing and Neighborhood Development, developers will get to build 250,000 units of market-rate housing in return for developing 50,000 affordable apartments. Thus, the reality of the "free" market is that private developers won't build any affordable housing unless they're guaranteed spectacular profits that come with market-rate apartments.

De Blasio's plan for pension fund investment in affordable housing will face the same basic problem. Either the investments generate profits, or there will be less money to pay city workers' pensions. Since the profit comes from market-rate housing, when the pension funds gain, affordable housing loses.

De Blasio's initiatives are a welcome change after Bloomberg actively making the lives of the homeless worse--but they won't meet the need for affordable housing in a city where, according to a Community Service Society study, 61 percent of low-income tenants paid at least half their income in rent in 2011. Or as the Community Service Society puts it: "What if making the rent left you with only $4.40 per day for everything else?"

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THE NEW mayor could do a great deal to at least preserve New York's largest source of affordable housing: rent regulation. There are more than 1 million rent-regulated apartments in New York City--47 percent of the housing stock--according to the New York City Housing and Vacancy Survey.

Rent increases in these apartments are set by the Rent Guidelines Board, which is appointed by the mayor. Bloomberg and his predecessor Rudolph Giuliani appointed people who could be counted on to reward landlords with outrageous increases every year. It didn't really matter if that made it harder for working people to make the rent.

Di Blasio can change that. He could appoint a Rent Guidelines Board that would give tenants what they really need--a rent freeze. That would go a long way toward preserving what's left of New York City's affordable housing.

But unless the New York state legislature acts soon, rent regulation could be as dead as the nickel fare on the subway.

Under current state law, landlords can immediately start charging the market rate any time they can get the rent for a vacant apartment above $2,500 a month. This vacancy decontrol means that any time a tenant leaves or dies, their apartment is bound to be deregulated. All the landlord has to do is file a form claiming they made some "improvements," like new windows or a new stove or refrigerator, and they can jack the rent up to $2,500.

David Jones, president of the Community Service Society, wrote in the New York Daily News that "the rate of loss now exceeds 13,500 rent stabilized [regulated] apartments every year. And because landlords are not required to report every apartment they take out of the stabilization system, the real number is certainly higher than that. Overall, between 2000 and 2007, the region lost 30 percent of the apartments that are affordable to low-income New Yorkers--an average of 50,000 apartments per year for seven years."

Every year, the governor and state legislature perform an elaborate dance with legislation to repeal vacancy decontrol. It passes the Democratic-dominated State Assembly, dies in the Republican-run State Senate, and Democratic Gov. Andrew Cuomo just wrings his hands.

Anyone who knows anything about New York state politics understands that it doesn't have to be this way. Cuomo could easily hold up the business-friendly legislation senate Republicans want until they repeal vacancy decontrol. Until now, he has never wanted to.

If de Blasio is genuinely concerned about affordable housing in New York City, he will go all-out to challenge his fellow Democrat. But he would need to go beyond issuing press releases--and mobilize people to take to the streets, not only in New York City, but the surrounding suburban counties that are also covered by rent regulation.

The only long-range answer to New York City's housing crisis is pressing the federal government to build new public housing for homeless and low-income people--something it hasn't done since the Nixon years in the 1970s. That would mean building a vibrant movement in cities and towns around the country.

In the next few months, Bill de Blasio's actions will reveal whether he is serious about housing for low- and moderate-income New Yorkers, or if that was all just campaign rhetoric.

In a footnote, Dasani had a moment in the sun when the new Public Advocate, Letitia James, was sworn in at City Hall. She brought Dasani on stage to hold the Bible and proclaim she was her new "best friend for forever." We'll find out if all this attention and publicity is enough to get at least one homeless family out of the shelters.